What is the equation of the line through (-2, 5) and (0, 3)? A. y = x - 3 B. y=x+3 C. y = -x + 3 D. y=-x-3​

To find the probability of getting 10 or more successes in a binomial experiment with p = 0.63 and n = 11 trials, we can use the cumulative probability function.

P(X ≥ 10) = 1 - P(X < 10)

Using a binomial probability formula, we can calculate the probability of getting exactly k successes:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where C(n, k) represents the binomial coefficient.

Let's calculate the probability for each value from 0 to 9 and subtract it from 1 to get the probability of 10 or more successes:

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)

P(X < 10) = Σ[C(11, k) * p^k * (1 - p)^(11 - k)] for k = 0 to 9

Using this formula, we can calculate the probability:

P(X < 10) ≈ 0.121

Therefore, the probability of getting 10 or more successes in the binomial experiment is:

P(X ≥ 10) ≈ 1 - P(X < 10) ≈ 1 - 0.121 ≈ 0.879

Rounding to three decimal places, the probability is approximately 0.879.

Learn more about Probability here -:brainly.com/question/13604758

#SPJ11

Answer:

The correct graph is graph B.

The magnitude of the number of the minutes in the school is 2.

Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.

There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).

The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.

On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.

The value storage is where you may find the number into the various magnetic.

As a result, the number of minutes spent in school is 2.

To learn more about order of magnitude from given link

https://brainly.com/question/15698632

#SPJ1

Complete question -

What is the Order of Magnitude of the number of minutes in a school day?

(-4,0)

-4 is in the y axis and 0 is in the x axis

Answer:

x = 35

Step-by-step explanation:

5 x 7 = 35

Answer: 35

Step-by-step explanation:

What you do is you multiply 5 and 7 and your answer is 35.

I hope I helped you with this. Have a great day!

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnhyrg

Step-by-step explanation:

Answer:x=15

Step-by-step explanation:

-angles of a triangle add up to make 180degrees

1) 34+7x+3x-4=180

2) 30+10x=180

3) subtract 30 from both sides

10x=150

4) divide both sides by 10

X=15

Main Answer:The approximate probability is 0.033

Supporting Question and Answer:

How do we calculate the expected average and standard deviation for a sample?

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

Body of the Solution:

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Final Answer:Therefore, the approximate probability is 0.033, accurate to three decimal places.

To learn more about the expected average and standard deviation for a sample  from the given link

https://brainly.com/question/31319458

#SPJ4

The approximate probability is 0.033

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Therefore, the approximate probability is 0.033, accurate to three decimal places.

To learn more about the expected average

brainly.com/question/31319458

#SPJ4

Answer:

$680

Step-by-step explanation:

Capacity of the truck: 4200 pounds and 480 cubic feet of cargo.

Small package: 25 pounds and 3 cubic feet each.

Large package: 50 pounds and 5 cubic feet each.

For x number of small packages:

25x pounds and 3x cubic feet

Let x = 8,

200 pounds and 24 cubic feet.

For y number of large packages:

50y pounds and 5y cubic feet

Let y = 80,

4000 pounds and 400 cubic feet.

Since delivery service charges $5 for each small package and $8 for each large package.

The maximum revenue per truck = ($5x + $8y)

                                                       = ( $5 x 8) + ($8 x 80)

                                                       = $680

Given:

The given function is:

\(y=-32x^2+90x+3\)

To find:

The range of the given function.

Solution:

We have,

\(y=-32x^2+90x+3\)

It is a quadratic function because the highest power of the variable x is 2.

Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.

If a quadratic function is \(f(x)=ax^2+bx+c\), then the vertex of the quadratic function is:

\(Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)\)

In the given function, \(a=-32,b=90,c=3\).

\(\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}\)

\(\dfrac{-b}{2a}=\dfrac{-90}{-64}\)

\(\dfrac{-b}{2a}=\dfrac{45}{32}\)

The value of the given function at \(x=\dfrac{45}{32}\) is:

\(y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3\)

\(y=\dfrac{2121}{32}\)

The vertex of the given downward parabola is \(\left(\dfrac{45}{32},\dfrac{2121}{32}\right)\). It means the maximum value of the function is \(y=\dfrac{2121}{32}\). So,

\(Range=\left\{y|y\leq \dfrac{2121}{32}\right\}\)

\(Range=\left(-\infty, \dfrac{2121}{32}\right ]\)

Therefore, the range of the given function is \(\left (-\infty, \dfrac{2121}{32}\right ]\).

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%.

Human blood is categorized into four types which are A, B, AB, and O. The percentages of Americans who have each of the four types are given below:

O - 43% A - 40% B - 12% AB - 5%

To calculate probabilities for various scenarios, we can use these percentages as follows.

a. The probability of a randomly selected American having type B blood is 12%.

b. The probability of a randomly selected American having type AB or O blood is 48%. The combined percentage of O and AB blood types is 48%. We can therefore say that the probability of an American having O or AB blood is 48%.

c. The probability of a randomly selected American not having type O blood is 55%. The percentage of Americans who don't have type O blood is the sum of percentages of A, B, and AB blood types, which is  Hence, the probability of not having O blood is lower than 57%. Therefore, the probability of a randomly selected American not having type O blood is 57%.

Learn more about Probability here:

brainly.com/question/13604758

#SPJ11

Answer:

7

Step-by-step explanation:

Answer:

I think it is d

Step-by-step explanation:

Answer:

x-6/x²-x-30

Step-by-step explanation:

(x-6)(x+5)

x²-x-30

when you factor out  x-6 you have a removable discontinuity and you have x+5 as your denominator and that would be the vertical asymptote since you can have a 0 as your denominator the V.A. would be x = -5.

The degree measure of angle A is 90 degrees if the measure of angle A is three times as big as the measure of angle C and the measure of angle B is 30 degrees bigger than the measure of angle C.

Let x be the measure of angle C in degrees.

According to the problem statement, angle A is three times as big as angle C, measuring 3x degrees.

Angle B is 30 degrees bigger than angle C, so its measure is x + 30 degrees.

The sum of the measures of the angles in a triangle is always 180 degrees so that we can write:

A + B + C = 180

Substituting the expressions we found for the angles in terms of x, we get:

3x + (x + 30) + x = 180

Simplifying and solving for x, we get:

5x + 30 = 180

5x = 150

x = 30

Therefore, angle C has a measure of 30 degrees, angle B has an estimate of 30 + 30 = 60 degrees, and angle A has a measure of 3(30) = 90 degrees.

So the degree measure of angle A is 90 degrees.

To read more about the sum of angles of a triangle:

https://brainly.com/question/23688688

#SPJ4

The rate at which the light's projection moves along the wall when the light's angle is 20 degrees from perpendicular to the wall is approximately 1.078 feet per second.

Let's let t be the time elapsed since the light started rotating, and θ be the angle that the light makes with the perpendicular to the wall, as shown in the diagram. The rate at which the light's projection moves along the wall is given by the derivative of the horizontal distance between the projection point P and the foot of perpendicular Q, with respect to time t. Let's call this distance x.

From the diagram, we can see that:

tan(θ) = x / 12

Differentiating both sides with respect to time t, we get:

sec²(θ) dθ/dt = (dx/dt) / 12

We are given that the light completes one rotation every 2 seconds, which means that the angular velocity of the light is:

dθ/dt = 2π / (2 seconds) = π radians per second

Substituting this value and θ = 20° (converted to radians), we get:

sec²(20°) (π rad/sec) = (dx/dt) / 12

Simplifying:

(1/cos²(20°)) (π/2) = (dx/dt) / 12

Multiplying both sides by 12 and evaluating the left-hand side, we get:

dx/dt = 1.078 feet per second

As a result, when the light's angle is 20 degrees from perpendicular to the wall, the pace at which the projection advances along the wall is roughly 1.078 feet per second.

To know more about the Rotating light, here

https://brainly.com/question/19755269

#SPJ4

In one gram of substance 0.22 grams of nickel is present. Then the amount of nickel in the 35 grams of the substance is 7.7 grams.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

A single gram of a certain metallic substance has 0.52 grams of copper and 0.26 grams of zinc.

The remaining portion of the substance is nickel.

Let the gram of nickel be x. Then we have

\(\sf x + 0.52 + 0.26 = 1\)

\(\sf x = 0.22\)

0.22 grams of nickel.

Ben estimated that 0.2 gram of nickel is in 1 gram of the substance.

He used this to estimate the amount of nickel in 35 grams of the substance.

Then we have

\(\sf \rightarrow35 \times 0.2 = 7\)

We know that in 1 gram the amount of nickel is 0.22 gram. Then we have

\(\sf \rightarrow 35 \times 0.22 = 7.7\)

The amount of nickel in the 35 grams of the substance is 7.7 grams.

More about the ratio and the proportion link is given below.

brainly.com/question/14335762

6x + 7 = 8x -17

or, 6x - 8x = -17 -7

or, -2x = -24

or, x = -24/-2 = 12

Answer is 12

Answer:

Step-by-step explanation:

I'm assuming you're trying to solve this for x. We use the difference identity for cosine and rewrite:

\(cos(x-30)=cosxcos30+sinxsin30\) and simplify using the unit circle to help.

\(cosx(\frac{\sqrt{3} }{2})+sinx(\frac{1}{2})=0\\cosx(\frac{\sqrt{3} }{2})=-\frac{1}{2} sinx\\cosx=-\frac{1}{2}(\frac{2}{\sqrt{3} })sinx\\cosx=-\frac{1}{\sqrt{3} }sinx\\1=-\frac{1}{\sqrt{3} }\frac{sinx}{cosx}\\1=-\frac{1}{\sqrt{3} }tanx\\-\sqrt{3} =tanx\)

and on the unit circle, the angle where the tangent is negative square root of 3 is -60° which is also a positive 300°

Answer:

x = n*360° + 120°      or     x = n*360° + 300°

Step-by-step explanation:

cos(x-30°)=0

x-30° = 90° or x-30° = 270°

it means can be : x-30° = n*360° + 90°    or    x-30° =n*360° + 270°

x = n*360° + 120°      or     x = n*360° + 300°   n is integers

By using the method of reduction of order as in differential equation to find a second linearly independent solution of the: Equation x2y" + xy' – 9y = 0 (x > 0); yı(x) = x3 has general solution is y(x) = c1x^3 + c2x^(-2),

Equation  4y" – 4y' + y = 0; yı(x) = ex/2 general solution is y(x) = c1exp(x/2) + c2*exp(-x/2),

Equation x2y" – x(x + 2)y' + (x + 2)y = 0 (x > 0); yı(x) = x has general solution  y2(x) = (C3x^(3/2) + C4)e^(-x).

Equation (x + 1)y" - (x + 2)y' + y = 0 (x > -1); yı(x) = ex has the general solution y(x) = c1ex + [c2 - ln(|2x + 1|)/2]ex.

Using the method of reduction of order, assume a second solution of the form y2(x) = u(x)y1(x). Then we have:

y'1(x)u(x) + y1(x)u'(x) = 0

u'(x) = -y'1(x)u(x)/y1(x)

Integrating both sides:

ln|u(x)| = -ln|y1(x)| + C

u(x) = K/x^3

Plugging this into the differential equation:

x^2y'' + xy' - 9y = 0

x^2[u''(x)y1(x) + 2u'(x)y1'(x) + u(x)y1''(x)] + x[u'(x)y1(x) + u(x)y1'(x)] - 9u(x)y1(x) = 0

Simplifying and dividing by x^2y1(x):

u''(x) - 6/x^2 u(x) = 0

Equation r(r-1) - 6 = 0, which has roots r = 3 and r = -2. Therefore, the general solution is y(x) = c1x^3 + c2x^(-2).

Using the method of reduction of order, assume a second solution of the form y2(x) = u(x)y1(x). Then we have:

y'1(x)u(x) + y1(x)u'(x) = 0

u'(x) = -y'1(x)u(x)/y1(x)

Integrating both sides:

ln|u(x)| = -2ln|y1(x)| + C

u(x) = Kexp(-x/2)

Plugging this into the differential equation:

4y'' - 4y' + y = 0

4[u''(x)y1(x) + 2u'(x)y1'(x) + u(x)y1''(x)] - 4[u'(x)y1(x) + u(x)y1'(x)] + u(x)y1(x) = 0

Simplifying and dividing by 4y1(x):

u''(x) - u(x)/4 = 0

equation r^2 - 1/4 = 0, has roots r = 1/2 and r = -1/2. Therefore, the general solution is y(x) = c1exp(x/2) + c2*exp(-x/2).

Let y2(x) = v(x)y1(x), where v(x) is a function to be determined.

Then, y'2(x) = v'(x)y1(x) + v(x)y'1(x) and y"2(x) = v"(x)y1(x) + 2v'(x)y'1(x) + v(x)y"1(x).

Substituting y1(x) and y2(x) into the given differential equation, we get:

x^2(v"(x)y1(x) + 2v'(x)y'1(x) + v(x)y"1(x)) - x(x+2)(v'(x)y1(x) + v(x)y'1(x)) + (x+2)v(x)y1(x) = 0

Simplifying and dividing by x^2y1(x), we obtain:

v"(x) + (2/x - (x+2)/x^2)v'(x) + ((x+2)/x^2 - 1/x^2)v(x) = 0

Let u(x) = v'(x). Then, the above equation can be written as a first-order linear differential equation:

u'(x) + (2/x - (x+2)/x^2)u(x) + ((x+2)/x^2 - 1/x^2)v(x) = 0

Using an integrating factor of exp(∫[(2/x - (x+2)/x^2)dx]), we get:

u(x)/x^2 = C1 + C2∫exp(-2lnx)exp((x+2)/x)dx

u(x)/x^2 = C1 + C2/x^2e^(x+2)

v(x) = C3x^(1/2)e^(-x) + C4x^(-3/2)e^(-x)

Therefore, the second linearly independent solution is:

y2(x) = (C3x^(3/2) + C4)e^(-x)

41. (x + 1)y" - (x + 2)y' + y = 0, one solution y1(x) = ex.

We assume that the second solution has the form y2(x) = v(x)ex.

We can then find y2'(x) and y2''(x) as follows:

y2'(x) = v'(x)ex + v(x)ex

y2''(x) = v''(x)ex + 2v'(x)ex + v(x)ex

We can substitute y1(x) and y2(x) into the differential equation and simplify using the above expressions for y2'(x) and y2''(x):

(x + 1)[v''(x)ex + 2v'(x)ex + v(x)ex] - (x + 2)[v'(x)ex + v(x)ex] + v(x)ex = 0

Simplifying and dividing by ex, we get:

xv''(x) + (2x + 1)v'(x) = 0

This is a first-order linear differential equation, which we can solve using separation of variables:

v'(x) = -1/(2x + 1) dv/dx

Integrating both sides

v(x) = C1 - ln(|2x + 1|)/2

where C1 is a constant of integration.

Therefore, the second linearly independent solution is:

y2(x) = v(x)ex = [C1 - ln(|2x + 1|)/2]ex

So, the general solution is:

y(x) = c1ex + [c2 - ln(|2x + 1|)/2]ex

where c1 and c2 are constants of integration.

To know more about Differential equation;

https://brainly.com/question/28099315

#SPJ4

____The given question is incomplete, the complete question is given below:

In each of Problems 38 through 42, a differential equation and one solution yı are given. Use the method of reduction of or- der as in Problem 37 to find a second linearly independent solution y2. 38. x2y" + xy' – 9y = 0 (x > 0); yı(x) = x3 39. 4y" – 4y' + y = 0; yı(x) = ex/2 40. x2y" – x(x + 2)y' + (x + 2)y = 0 (x > 0); yı(x) = x 41. (x + 1)y" - (x + 2)y' + y = 0 (x > -1); yı(x) = ex

The amount of money that the person will have for a new bike by summer is $240.

From the information, the person opens a savings account and make a pact to deposit $30 a month. The person also has 8 months.

In this case, the total amount that will be in the account will be:

= Amount saved each month × Number of months

= $30 × 8

= $240

The person has $240.

Learn more about money on:

brainly.com/question/24373500

#SPJ1

Answer: 4/8 + 3/6 + 1/1

Step-by-step explanation: this is only if you can use the same number twice!!!

Answer:

She has 27 quarters

Step-by-step explanation:

Let:

x = Number of nickels

y = Number of quarters

US$0.05 = 5 cents = monetary value of a nickel

US$0.25 = 25 cents = monetary value of a quarter

                      x + y = 68

                     x = 68 - y  ---- --------  (equation i)

                0.05x + 0.25y = 8.80----- (equation ii)

These two are linear simultaneous equations, which can be solved either by substitution, elimination or graphical method.

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

0.05(68 - y) + 0.25y = 8.80

Expand the brackets by applying the Distributive Law and then bring all the like terms together. y needs to be isolated and made the subject of the equation:

= 3.4 - 0.05y + 0.25y = 8.80

= 0.25y - 0.05y = 8.80 - 3.40

= 0.20y = 5.40

= y = \(\frac{5.40}{0.20}\)

∴ y = number of quarters = 27

Answer:

29(!£6287&7&(&

Step-by-step explanation:

That's it ty

Answer:

The minimum is -4

Step-by-step explanation:

The minimum is the lowest point on the parabola

It is at (-3,-4)

The y value is the minimum of the function

The minimum is -4

Answer:

5 gallons because 13.5 divided by 5.4 is 2. 5 so times 2 so 5

Answer:

5 gallons.

Step-by-step explanation:

two gallons=$5.40

? gallons=$13.50

you cross multiply

2 × $13.50÷$5.40

27÷5.40=5 gallons

(a) The Nine elements following (0, 0) are: (0, 1), (1, 1), (2, 1), (3, 1), (1, 2), (2, 2), (3, 2), (2, 3), and (3, 3).

(b) False; a counterexample is (2,3) which is in the set but violates the claim that m ≤ 2 for all (m, ) ∈ .

(a) The nine elements following (0, 0) in are:

(0, 1), (1, 1), (2, 1), (3, 1), (1, 2), (2, 2), (3, 2), (2, 3), (3, 3).

To see why, we use the definition of as given in (ii): starting with (0, 0), we can add (0, 1), then (1, 1) and (2, 1), which gives us three elements in the first row.

Then we can add (1, 2), (2, 2), and (3, 2) to get three more elements in the second row.

Finally, we add (2, 3) and (3, 3) to get the two elements in the third row, for a total of nine elements.

(b) False.

To see why, consider the element (2, 3). By definition (ii), if (m, ) ∈ , then (m + 2, + 1) ∈ .

So if (2, ) ∈ , then (4, 4) ∈ , which means that (4, 3) and (3, 4) must also be in .

But (3, 4) cannot be in , because it violates the condition that the second coordinate is at most one more than the first.

Therefore, (2, ) is not in , and we have a counterexample to the claim that m ≤ 2 for all (m, ) ∈ .

In fact, we can explicitly construct elements of for any m and : starting with (m, ), we add (m, + 1), then (m + 1, + 1) and (m + 2, + 1), and so on, until we reach a point where the second coordinate is too large to satisfy the condition.

This shows that there are infinitely many elements of with any given value of m.

For similar question on construct elements.

https://brainly.com/question/30629254

#SPJ11

True.
For any element (m, n) in the subset , we know that m and n are both natural numbers (elements of N).
Let's assume that (m, ) ∈  such that m > 2.
Then, we can say that there are at least three elements in N (0, 1, and 2) that are less than or equal to m.
Since  is a subset of N × N, this means that there are at least three ordered pairs (i, j) in  such that i ≤ m.
However, we know that  only contains ordered pairs where the second element is 9.
This contradicts our assumption that (m, ) ∈ , since we cannot have any ordered pairs in  such that the first element is greater than 2.
Therefore, we can conclude that if (m, ) ∈ , then m ≤ 2.
Hi! Your question seems to be missing some crucial information, but I'll do my best to explain the concept of subsets and elements using the number nine.

A subset is a set that contains some or all elements of another set, without any additional elements. In the context of the set N = {0, 1, 2, 3, ...}, a subset could be any collection of these elements.

Elements are the individual members within a set. In set N, elements include 0, 1, 2, 3, and so on. The number nine is also an element of the set N.

For the true or false statement you provided, it appears to be incomplete. If you can provide the complete statement or question, I'd be happy to help you further.

The utility of bundle (4,6) for Mark, given the utility function U(x,y) = min{2x, 3y}, is 12.

the utility of bundle (4,8) for Mark is also 12.

For Rob's utility function U(x,y) = 3x + 2y, the utility of bundle (3,4) is 17.

The utility of bundle (4,6) for Mark, given the utility function U(x,y) = min{2x, 3y}, is 12. The utility is determined by taking the minimum value between 2 times the quantity of good x (2x) and 3 times the quantity of good y (3y). In this case, 2 times 4 is 8, and 3 times 6 is 18. Since the minimum value is 8, the utility of bundle (4,6) is 8.

Similarly, the utility of bundle (4,8) for Mark is 12. Again, we compare 2 times 4 (8) with 3 times 8 (24). The minimum value is 8, resulting in a utility of 8 for the bundle (4,8).

For the second part of the question, we'll now consider Rob's utility function: U(x,y) = 3x + 2y. The utility of bundle (3,4) for Rob can be calculated as follows: 3 times 3 (9) plus 2 times 4 (8), which equals 17. Therefore, the utility of bundle (3,4) for Rob is 17.

Indifference curves represent combinations of goods that yield the same level of utility for an individual. Since the utility function U(x,y) = 3x + 2y is a linear function, the indifference curve passing through the bundle (3,4) will be a straight line with a negative slope.

It implies that as one good increases, the other must decrease in a specific ratio to maintain the same level of utility. By plotting different bundles that yield the same utility level of 17, we can draw the indifference curve through the point (3,4).

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ11

Answer:

The answer is above. Numbers 2 and 3

The recursive formula that represents the value of account is a (n) = 1.0194 ;a (n-1); V (0) = 3.38.

Any term of a series can be defined by its preceding term in a recursive formula (s).

The general formula to find recursion is \(a_{n}= ra_{n-1}\) where r is the common ratio and n should ne grater than 2.

a (n) = 3.38. a (n-1);a (1) = 1.0194

a(n) = 3.38. a (n - 1);a (0) = 1.0194

a(n) = 1.0194. a (n-1);a (1) = 3.38

a (n) = 1.0194 .a (n-1); a (0) = 3.38

To learn more about recursion visit the link:

https://brainly.com/question/20749341

#SPJ1